Distance & Displacement

Problems

practice

A mountain climbing expedition establishes a base camp and two intermediate camps, A and B. Camp A is 11,200 m east of and 3,200 m above base camp. Camp B is 8,400 m east of and 1,700 m higher than Camp A. Determine the displacement between base camp and Camp B.

A laser beam is aimed 15.95° above the horizontal at a mirror 11,648 m away. It glances off the mirror and continues for an additional 8570. m at 11.44° above the horizon until it hits its target. What is the resultant displacement of the beam to the target?

Three of the four busiest airports in the US are Hartsfield-Jackson in Atlanta, Georgia (ATL), O'Hare in Chicago, Illinois (ORD), and Dallas/Fort Worth in Texas (DFW). Complete the following table for roundtrip airplane journey from Atlanta to Chicago to Dallas to Atlanta. Note: Headings are measured clockwise from due north.

departure

arrival

distance

heading

ATL

ORD

975 km

342.8°

ORD

DFW

1291 km

221.6°

DFW

ATL

round trip

n/a

Calculate both the distance and the magnitude of the displacement of the earth after…

one complete orbit around the sun

one-half orbit around the sun

one-fourth orbit around the sun

What relationship between distance and displacement does this illustrate?

conceptual

For each of the following questions, decide whether the questioner is asking for the distance or the magnitude of the displacement (or either or neither).

How far do you walk each day?

How far is it from Toronto to Mexico City by airplane?

How far is it from Toronto to Mexico City by car?

How far is the earth from the moon?

How long is a standard sheet of plywood?

How long is the coastline of Britain?

How long is the Nile?

How long is the track on a compact disc?

How long did it take you to get here?

How many frequent flyer miles do you have?

What is the radius of the earth?

numerical

An ambitious hiker walks 25 km west and then 35 km south in a day. Find the magnitude and direction of the hiker's resultant displacement (relative to due west).

I went for a walk the other day. I went four avenues east (0.80 miles), then twenty-four streets south (1.20 miles), then one avenue west (0.20 miles), and finally eight streets north (0.40 miles).

In the fictitious city of Metropolis, streets run east-west while avenues run north-south. The separation between centers for both the streets and the avenues is 100 m, resulting in square city blocks. Superman is located at 33rd Street and 3rd Avenue while Lois Lane is located north and east of Superman at 45th Street and 12th Avenue.

How far would Lois Lane have to walk to reach Superman?

How far would Superman have to fly to reach Lois Lane?

In what direction should Superman fly to reach Lois Lane as quickly as possible?